Apparatus and Method for Detecting a Brush Liftoff in a Synchronous Generator Rotor Circuit

ABSTRACT

An apparatus and method detects an open condition of a grounding path provided by a rotor grounding brush electrically connecting a rotor body of a rotor to electrical ground. The rotor includes an insulated field winding wrapped around the rotor body and is configured to generate a magnetic field upon receipt of an exciter voltage across lower and upper extremities of the insulated field winding. The method includes applying a square wave voltage signal to a second end of each of a first and a second buffer resistor, where a first end of each of the buffer resistors is operatively connected to respective upper and lower leads of the exciter voltage source, and calculating the total capacitance between the insulated field winding and electrical ground. The total capacitance when compared to a pre-selected capacitance value is determinative of the absence of the grounding path.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional application of a U.S. patentapplication having Ser. No. 11/510,352, entitled An Apparatus and Methodfor Detecting a Brush Liftoff in a Synchronous Generator Rotor Circuit,filed 25 Aug. 2006 naming Gabriel Benmouyal and Thanh-Xuan Nguyen asinventors.

BACKGROUND OF THE INVENTION

The present invention generally relates to synchronous generators, andmore specifically, to an apparatus and method for detecting a brushliftoff in a synchronous generator rotor circuit.

Synchronous electrical generators (“synchronous generators”) are used inelectric utility systems to convert mechanical rotation (e.g., shaftrotation provided by a steam turbine) into alternating electric currentvia well-known electromagnetic principles. After suitable conditioning,the alternating electrical current is typically transmitted anddistributed to a variety of power system loads.

In general, synchronous generator design is based on Faraday's law ofelectromagnetic induction and includes a rotating rotor driven by anexternal torque for inducing an electromagnetic field (EMF) in astationary stator. The rotor includes a field winding wrapped around arotor body, and the stator includes an armature winding wrapped aroundan armature body.

In operation, a direct current is made to flow in the field winding togenerate a magnetic field. When the rotor is made to rotate, themagnetic field rotates with it, passing through the stator winding(s)and inducing an electric current therein.

Insulation material is utilized to cover the field winding(s) in orderto electrically isolate the field winding(s) from the rotor body. As isknown, detecting a loss of the insulation covering the field winding(s),or a field ground, is vital to ensuring reliable operation of thesynchronous generator. While a field ground of insulation at one pointalong the field winding may be inconsequential to operation, fieldgrounds at two locations along the field winding could result in seriousdamage to the synchronous generator.

One method used to achieve a field-ground protection is the so-calledswitched-DC injection method. One implementation of a switched-DCinjection method is illustrated on page 61 of a Siemens AG instructionmanual, entitled “Numerical Machine Protection 7UM515,” version v3.1,dated 1996, the complete disclosure thereof being incorporated herein byreference. A variation of the switched-DC injection method is alsodescribed in U.S. Pat. No. 6,794,879, entitled “Apparatus and Method forDetecting and Calculating Ground Fault Resistance,” issued on Sep. 24,2004, naming Lawson et al. as inventors, the complete disclosure thereofbeing incorporated herein by reference. Unlike other switched-DCinjection methods where a voltage is measured across a grounded “senseresistor” in order to determine a loss of field winding insulation, the'879 patent discloses using a voltage controlled oscillator (VCO)configured to measure a differential voltage across a floating senseresistor.

The switched-DC injection method requires that the rotor body beconnected to electrical ground. This is typically accomplished by meansof a (rotor) grounding brush. When the grounding brush no longerprovides a low resistance circuit between the rotor body and electricalground, “brush liftoff” has occurred, and the device performing thefield-ground protection is no longer able to perform its task. Detectingsuch a brush liftoff, or open condition of the grounding path providedby the grounding brush, is therefore critical to reliable synchronousgenerator operation. The present invention provides such protection.

SUMMARY OF THE INVENTION

The invention is directed to a system and method for providing detectionof a brush liftoff in a synchronous generator rotor circuit bymonitoring and evaluating the capacitance between the field winding andelectrical ground. A brush liftoff is declared when the monitoredcapacitance value undergoes a drastic reduction from its steady statecapacitance value.

In accordance with one embodiment of the invention, a system fordetecting brush liftoff in an electrical generator of the type whichincludes a rotor with an electrically conductive rotor body and aninsulated field winding, the insulated field winding being wrappedaround the rotor body and connected to receive an exciter voltage atfirst and second exciter nodes, and a rotor grounding brush electricallycoupling the rotor body to electrical ground, includes first and secondbuffer resistors R each coupled at one end to a common node and at theiropposite ends to respective ones of the first and second exciter nodes.The system further includes a signal generator coupled to apply aperiodic oscillating voltage signal to the common node, a sense resistorR_(S) coupling the signal generator to electrical ground, and a low-passfilter. The input of the low-pass filter is coupled across the senseresistor to receive positive and a negative sense resistor voltagesVRS_(P) and VRS_(N). The low-pass filter develops a filtered positivesense resistor voltage signal VRS_(P) _(—) lp and a filtered negativesense resistor voltage signal VRS_(N) _(—) lp. These signals are appliedto a microcontroller programmed to calculate a total capacitance C_(FG)between the insulated field winding and electrical ground from which anopen rotor grounding circuit can be detected. The total capacitance isdetermined by taking an integrated value of a plurality of voltagesamples divided by a proportionality constant, where the plurality ofvoltage samples are derived from the filtered positive sense resistorvoltage signal VRS_(P) _(—) lp during a positive one-half period of theperiodic oscillating voltage signal, and the filtered negative senseresistor voltage signal VRS_(N) _(—) lp during a negative one-halfperiod of the periodic oscillating voltage signal.

In accordance with another embodiment of the invention, a method fordetecting an open condition of a grounding circuit provided by a rotorgrounding brush electrically connecting an electrically conductive bodyof a rotor to electrical ground includes a rotor having an insulatedfield winding wrapped around the electrically conductive body where theinsulated field winding is coupled to receive an exciter voltage atfirst and second exciter nodes, includes applying a periodic oscillatingvoltage signal to a common node between first and second bufferresistors, coupling the exciter voltage to the first and second bufferresistors, calculating a total capacitance C_(FG) between the insulatedfield winding and electrical ground, and determining from the totalcapacitance whether an open condition exists in the grounding circuit.

In accordance with a further embodiment of the invention, a method fordetecting an open condition of a grounding circuit provided by a rotorgrounding brush electrically connecting a rotor body of a rotor toelectrical ground, wherein the rotor has an insulated field windingwrapped around the rotor body and the insulated field winding isconfigured to generate a magnetic field upon receipt of an excitervoltage from a voltage exciter connected at first and second exciternodes at respective upper and lower extremities of the insulated fieldwinding, includes applying a square wave voltage signal to a second endof each of a first and a second buffer resistor. A first end of each ofthe first and second buffer resistors is operatively connected torespective first and second exciter nodes. The method further includesintegrating a voltage sample of a plurality of voltage samples over oneof a positive and a negative one-half period of the square wave voltagesignal to form an integrated value, and dividing the integrated value bya proportionality constant to calculate a total capacitance C_(FG)between the insulated field winding and electrical ground, and declaringthe open condition of the grounding path if the total capacitance isless than a pre-selected capacitance setting.

It should be understood that the present invention includes a number ofdifferent aspects and/or features which may have utility alone and/or incombination with other aspects or features. Accordingly, this summary isnot an exhaustive identification of each such aspect or feature that isnow or may hereafter be claimed, but represents an overview of certainaspects of the present invention to assist in understanding the moredetailed description of preferred embodiments that follows. The scope ofthe invention is not limited to the specific embodiments describedbelow, but is set forth in the claims now or hereafter filed.

BRIEF DESCRIPTION OF THE DRAWINGS

Although the characteristic features of this invention will beparticularly pointed out in the claims, the invention itself, and themanner in which it can be made and used, can be better understood byreferring to the following description taken in connection with theaccompanying drawings forming a part hereof, wherein like referencenumerals refer to like parts throughout the several views and in which:

FIG. 1 is a single line schematic diagram of a synchronous generatorrotor assembly which incorporates a switched-DC injection circuit forfield ground protection, shown under normal grounding conditions.

FIG. 2 is an electrical equivalent circuit of the synchronous generatorrotor assembly of FIG. 1, shown in a steady state.

FIG. 3 is an electrical equivalent circuit of a switched-DC portion ofthe synchronous generator rotor assembly of FIG. 2 in a transient state,shown under normal grounding conditions.

FIG. 4 is a graphical diagram of an exemplary transient waveformgenerated across a sense resistor of the electrical equivalent circuitof FIG. 3, shown under normal grounding conditions.

FIG. 5 is a schematic diagram of a synchronous generator rotor assemblywhich incorporates a switched-DC injection circuit for field groundprotection, shown under abnormal grounding conditions.

FIG. 6 is an electrical equivalent circuit of a switched-DC portion ofthe synchronous generator rotor assembly of FIG. 5 in a transient state,shown under abnormal grounding conditions.

FIG. 7 is a schematic diagram illustrating a field ground moduleconstructed in accordance with one embodiment of the invention.

FIG. 8 is a functional block diagram illustrating a method formonitoring the capacitance between the field winding and electricalground of a synchronous generator rotor assembly to determine a brushliftoff condition, in accordance with one embodiment of the invention.

FIG. 9 is a functional block diagram of a mathematical simulationillustrating that inclusion of a low-pass filter in the synchronousgenerator rotor assembly of FIG. 5 does not affect the proportionalitybetween an integral of a sense resistor voltage and a capacitancebetween the field winding and electrical ground.

FIG. 10 is a graphical comparison of an integrated transient waveformand an integrated filtered transient waveform generated as a result ofimplementation of the mathematical simulation illustrated in FIG. 9.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to the Drawings, and particularly to FIG. 1, a synchronousgenerator rotor assembly 150 incorporates a switched-DC injectioncircuit for field ground protection. The rotor assembly 150 includes arotor body 152 coupled to electrical ground 154 via a grounding brush156. The rotor body 152 is preferably formed from a conductive material,such as steel. A field winding 158, covered by an electricallyinsulating material, is wrapped around rotor body 152. When an excitervoltage V_(FD) at 160 is applied at first and second exciter nodes 161and 163 located at respective upper and lower winding extremities, amagnetic field is generated in and around rotor assembly 150.

To detect grounding of the field winding 158 a square wave voltagesignal 164 is applied to first and second exciter nodes 161 and 163 onthe field winding via buffer resistors R166. Signal 164 has a frequencyF_(DC) and provides positive and negative injected DC voltages VDC_(P)167 and VDC_(N) 169, respectively (i.e., injected switched-DC current).The period T_(DC) of signal 164 corresponds to switching frequencyF_(DC), and therefore during the period T_(DC), each of the positive andnegative injected DC voltages VDC_(P) and VDC_(N) are applied torespective exciter nodes 161, 163 during an interval equal to one-halfof the period T_(DC) or T_(DC)/2 186. As illustrated, a low pass filter171 is also included in the synchronous generator rotor assembly 150 toprovide electrical noise abatement.

The synchronous generator rotor assembly 150 has a resistance R_(X)between rotor body 152 and field winding 158; a resistance R_(S) betweena circuit node receiving the square wave voltage signal 164 andelectrical ground 154; and a capacitance C_(FR) between field winding158 and rotor body 152. Under normal conditions (i.e., no brushliftoff), a capacitance value represented by the field capacitor C_(FR)174 is equal to the capacitance between field winding 158 and electricalground 154.

Referring to the electrical equivalent circuit of FIG. 2, if insulationresistor R_(X) 170 has a substantially infinite value indicating no lossof field winding insulation, the voltage across the sense resistor R_(S)172 is substantially zero upon application of square wave signal 164 asno DC current will flow. In that case, at the end of the positivehalf-period of signal 164, the positive sense resistor voltage VRS_(P)165 a across sense resistor R_(S) 172 is zero. Similarly, at the end ofthe negative half-period of signal 164, the negative sense resistorvoltage VRS_(N) 165 b across sense resistor R_(S) 172 is zero. As aresult, the magnitude of both of the filtered positive sense resistorvoltage signal VRS_(P) _(—) lp 102 a and the filtered negative senseresistor voltage signal VRS_(N) _(—) lp 102 b are substantially zero atthe end of the corresponding half-period.

Conversely, if insulation resistor R_(X) 170 has a value indicating aloss of field winding insulation, a significant voltage will developacross sense resistor R_(S) 172 upon application of signal 164 as DCcurrent will flow. In that case, at the end of the positive half-periodof signal 164, a positive sense resistor voltage VRS_(P) 165 a developsacross the sense resistor R_(S) 172. Similarly, at the end of thenegative half-period of signal 164, a negative sense resistor voltageVRS_(N) 165 b develops across sense resistor R_(S) 172. The magnitude ofboth of the filtered positive sense resistor voltage signal VRS_(P) _(—)lp 102 and the filtered negative sense resistor voltage signal VRS_(N)_(—) lp 103 will therefore have a significant non-zero value at the endof the corresponding one-half period. A brush liftoff determination ismade at the end of every interval of time corresponding to the one-halfperiod T_(DC)/2 186, using integrated values of voltages of filteredpositive sense resistor voltage signal VRS_(N) _(—) lp 102 a andfiltered negative sense resistor voltage signal 102 b VRS_(N) _(—) lp.It should be noted that the values of sense resistor R_(S) 172 and eachof the buffer resistors R 166 are fixed while the value of theinsulation resistor R_(X) 170 varies.

For ease of discussion, the following variables may be defined where:

-   -   VDC_(P) (167)=positive injected DC voltage, injected during        positive half-period    -   VDC_(N) (169)=negative injected DC voltage, injected during        negative half-period    -   VRS_(P) (165 a)=sense resistor voltage during positive        half-period    -   VRS_(N) (165 b)=sense resistor voltage during negative        half-period    -   VRS_(P) _(—) lp (102)=filtered sense resistor voltage signal        during positive half-period    -   VRS_(N) _(—) lp (103)=filtered sense resistor voltage signal        during negative half-period    -   VFD_(P) (160 a)=measured exciter voltage at the end of the        positive half-period    -   VFD_(N) (160 b)=measured exciter voltage at the end of the        negative half-period    -   R_(S)=sense resistor (172)    -   R=buffer resistors (166)    -   Rx=insulation resistor (170)    -   x=relative distance to a fault (varies between 0 and 1)

Referring again to FIG. 4, if it is assumed that the measured excitervoltage at the end of the positive half-period VFD_(P) 160 a and themeasured exciter voltage at the end of the negative half-period VFD_(N)160 b are equal with respect to time periods, resolving the electricalequivalent circuit of FIG. 2 yields the following equation for a valueof the unknown insulation resistor R_(X) 170:

$\begin{matrix}{R_{X} = {\frac{R_{S}( {{VDC}_{P} - {VDC}_{N}} )}{{VRS}_{P} - {VRS}_{N}} - ( {\frac{R}{2} + R_{S}} )}} & (1)\end{matrix}$

Alternatively, if the value of excitation voltage VFD_(P) 160 a at theend of the positive half-cycle and excitation voltage VFD_(N) 160 b atthe end of the negative half-cycle are not assumed to be equal, theinsulation resistance can be computed using Equation (2), taking intoaccount the change into the excitation voltage:

$\begin{matrix}{R_{X} = {\frac{R_{S}( {{\frac{{VFD}_{N}}{{VFD}_{P}}{VDC}_{P}} - {VDC}_{N}} )}{{\frac{{VFD}_{N}}{{VFD}_{P}}{VRS}_{P}} - {VDC}_{N}} - ( {\frac{R}{2} + R_{S}} )}} & (2)\end{matrix}$

Equation (2) may be expressed otherwise by introducing the distance tothe fault x (varying between 0 and 1) as a variable:

$\begin{matrix}{R_{X} = {\frac{{R_{S}( {{VDC}_{P} - {VDC}_{N}} )} + {\frac{R_{S}}{2}( {{2x} - 1} )( {{VFD}_{P} - {VFD}_{N}} )}}{{VRS}_{P} - {VDC}_{N}} - ( {\frac{R}{2} + R_{S}} )}} & (3)\end{matrix}$

Equations (1) through (3) assume that the electrical equivalent circuitof FIG. 2 represents a steady state condition (i.e., the transientsignal that is caused by the application of a DC voltage across acapacitor in series with resistor has faded away). In reality, however,when either the positive or the negative injected DC voltage VDC_(P) 167or VDC_(N) 169 is applied to the first and second exciter nodes 161 and163 respectively, the voltage across the sense resistor R_(S) 172undergoes a transient state (i.e., the positive and negative senseresistor voltages VRS_(P) 165 a and VRS_(N) 165 b) before it settlesinto a steady state.

The nature of such a transient voltage may be represented by FIG. 3,which illustrates an electrical equivalent circuit of the switched-DCportion of rotor assembly 150 in a transient state, with the groundingbrush 156 electrically connecting rotor body 152 to electrical ground154. As illustrated, FIG. 3 represents an application of a DC voltageacross the field capacitor C_(FR) 174 in series with the bufferresistors R 166. It is assumed that the field winding resistance isnegligible as compared to the sum of the buffer resistors R 166 plus thesense resistor R_(S) 172.

When the positive injected DC voltage VDC_(P) 167 is first applied tothe switched-DC portion of rotor assembly 150, the transient voltageacross the sense resistor R_(S) 172 will be an exponentially decayingwaveform. For example, FIG. 4 is a graphical depiction of an exemplarypositive transient waveform 184 generated across sense resistor R_(S)172 of the electrical equivalent circuit of FIG. 3, with the groundingbrush 156 electrically connecting rotor body 152 to electrical ground154. The positive transient waveform 184 is a result of the positivesense resistor voltage VRS_(P) 165 a and its subsequent exponentialdecay to a steady state. Referring to FIGS. 2, 3 and 4, the positivesense resistor voltage VRS_(P) 165 a equals a peak positive senseresistor voltage times a decaying exponential function:

$\begin{matrix}{{VRS}_{P} = {{VRS}_{PEAK}*^{\frac{1}{\tau_{FIRST}}}}} & (4)\end{matrix}$

-   -   where VRS_(peak) corresponds to the highest value of the        exponentially decaying transient waveform that begins at the        start of each one-half period T_(DC)/2 186, and where a first        time constant τ_(FIRST), or a pre-brush liftoff time constant,        is equal to:

τ_(FIRST)=(R+R _(S))*C _(FR)  (5)

Referring to Equation (3), field capacitor C_(FR) 174 is representativeof the capacitance between field winding 158 and the rotor body 152.Because rotor body 152 is connected to electrical ground 154 viagrounding brush 156, however, the capacitance value represented by fieldcapacitor C_(FR) 174 is also equal to the capacitance between fieldwinding 158 and electrical ground 154.

The voltage across sense resistor R_(S) 172 will also be a negativetransient waveform 187 when the negative injected DC voltage VDC_(N) 169is applied to the electrical equivalent circuit of the switched-DCportion of rotor assembly 150. It should be noted that the voltageacross sense resistor R_(S) 172 is assumed to go to zero in a steadystate. A zero voltage across sense resistor R_(S) 172 corresponds to thesituation where the insulation resistor R_(X) 170 has very high valueclose to infinity and is therefore properly isolating field winding 158from the electrical ground 154.

FIGS. 1-3 illustrate a situation where no brush liftoff has occurred.When brush liftoff occurs, however, rotor body 152 is no longerconnected to electrical ground 154 via the grounding brush 156. FIG. 5is another schematic diagram of a rotor assembly 190 that incorporates aswitched-DC injection circuit for field ground protection, with thegrounding brush 156 disconnected from rotor body 152. Unlike thesynchronous rotor assembly of FIG. 1, rotor body 152 is connected toelectrical ground 154 via a capacitance represented as a new capacitorC_(RG) 192. In that case, the capacitance value represented by the fieldcapacitor C_(FR) 174 typically ranges from 0.1 to 2 microfarads, whilethe capacitance value represented by capacitor C_(RG) 192 is on theorder of a few nanofarads.

FIG. 6 is an electrical equivalent circuit of the switched-DC portion ofrotor assembly 190 in a transient state, with grounding brush 156disconnected from rotor body 152. As illustrated, field capacitor C_(FR)174 is in series with capacitor C_(RG) 192. Because the capacitancevalue represented by capacitor C_(RG) 192 is typically much smaller thanthe capacitance value represented by field capacitor C_(FR) 174, thevalue of the resulting total capacitance represented as capacitor C_(FG)194 (i.e., the field capacitor C_(FR) 174 in series with the newcapacitance C_(RG) 192) will be much smaller than the pre-brush liftoffcapacitance value represented by field capacitor C_(FR) 174.

Because rotor body 152 is now connected to electrical ground 154 viacapacitor C_(RG) 192, due to the brush liftoff condition, a second timeconstant τ_(SECOND), or a post-brush liftoff time constant, may bedefined as:

$\begin{matrix}{\tau_{SECOND} = {( {R + R_{S}} )( \frac{C_{{FR}\;}*C_{RG}}{C_{FR} + C_{RG}} )}} & (6)\end{matrix}$

where the capacitance value represented by capacitor C_(FG) 194 is muchsmaller than the pre-brush liftoff capacitance value represented byfield capacitor C_(FR) 174. As a result, the post-brush liftoff timeconstant τ_(SECOND) will be much smaller than the pre-brush liftoff timeconstant τ_(FIRST). Accordingly, an exponentially decaying transientsignal will decay more quickly and the voltage across sense resistorR_(S) 172 will settle to its steady state final value of zero much morerapidly.

In accordance with the invention, the filtered positive and negativesense resistor voltage signals 102 and 103 in a transient-state are usedto determine an occurrence of a brush liftoff condition. Morespecifically, the positive and negative voltage signals across senseresistor R_(S) 172 are processed through low-pass filter 171 to form thefiltered positive sense resistor voltage signal VRS_(P) _(—) lp 102 andthe filtered negative sense resistor voltage signal VRS_(N) _(—) lp 103.Then, as shown in Equations (1)-(6), the capacitance observed betweenfield winding 158 and electrical ground 154 can be determined andutilized as an indicator of a brush liftoff or open condition of thegrounding path.

FIG. 7 is a schematic diagram illustrating a field ground detectionmodule 100, constructed in accordance with an embodiment of theinvention. As illustrated, module 100 includes an input configured toreceive filtered positive and negative sense resistor voltage signals102 and 103 from switched-DC injection circuit 150 (discussed below inconnection with FIG. 3). An analog-to-digital (A/D) converter 104 thenmultiplexes, samples and digitizes the filtered positive and negativesense resistor voltage signals 102 to form digitized voltage signals 106suitable for use by a microcontroller 110. In a preferred embodiment,microcontroller 110 includes a CPU, or a microprocessor 112, a programmemory 114 (e.g., a Flash EPROM) and a parameter memory 116 (e.g., anEEPROM). As will be appreciated by those skilled in the art, othersuitable microcontroller configurations may be utilized. Further,although discussed in terms of a microcontroller, it should be notedthat the embodiments presented and claimed herein may be practiced usingan FPGA (field programmable gate array) or other equivalent.

The microprocessor 112, executing a computer program or voltage controllogic scheme (discussed below in connection with FIG. 8), processes(each of) the digitized voltage signals 106, representative of thefiltered positive and negative sense resistor voltage signals 102 and103, to determine whether a field winding insulation problem hasoccurred and whether a brush liftoff has occurred. A binary contactoutput 118 actuates an alarm indication (e.g., an audio or visual alarm)to indicate a brush liftoff.

FIG. 8 illustrates a method 200 for monitoring the capacitance betweenfield winding 158 and the electrical ground 154, by processing thefiltered positive and negative sense resistor voltage signals VRS_(P)_(—) lp and VRS_(N) _(—) lp to determine a brush liftoff.

As shown by FIG. 8, the method 200 begins when the microcontroller 110is cyclically interrupted (step 202). An interrupt marks the beginning(or the end) of a predetermined interval. Although preferably selectedto be between 0.1 and 1 milliseconds, the predetermined interval may beany suitable fixed frequency that enables effective monitoring of thecapacitance between the field winding 158 and electrical ground 154. Inan example, 500 interrupts will occur during a one-half period T_(DC)/2186 of 500 milliseconds, when the predetermined interval is selected tooccur every 1 milliseconds.

Upon each interrupt, the microcontroller 110 measures either thefiltered positive sense resistor voltage signal VRS_(P) _(—) lp 102 orthe filtered negative sense resistor voltage signal VRS_(N) _(—) lp 103to form a voltage sample of the positive or negative filtered senseresistor voltage signal (step 204). One voltage sample is measured uponeach interrupt. As noted above, the filtered positive and negative senseresistor voltage signals in their transient state represent the voltageacross sense resistor R_(S) 172 during application of square wavevoltage signal 164, subsequently filtered via the low-pass filter 171.Accordingly, the filtered positive sense resistor voltage signal VRS_(P)_(—) lp 102 is sampled during application of the positive injected DCvoltage VDC_(P) 167 portion of square wave voltage signal 164, while thefiltered negative sense resistor voltage signal VRS_(N) _(—) lp 103 issampled during application of negative injected DC voltage VDC_(N) 169portion of signal 164. For ease of discussion, the remaining steps ofthe method 200 will be described in terms of the filtered positive senseresistor voltage signal VRS_(P) _(—) lp 102, it being understood thatthe method steps are equally applicable to the filtered negative senseresistor voltage signal VRS_(N) _(—) lp 103.

Next, the microcontroller 110 integrates using the voltage samplesmeasured from the filtered positive sense resistor voltage signalVRS_(P) _(—) lp 102 over an interval of time equal to the one-halfperiod T_(DC)/2 186 (step 206). The integration is accomplished bysumming the instantaneous samples of the filtered positive senseresistor voltage signal VRS_(P) _(—) lp 102 in the transient-stateduring the interval of time equal to the one-half period T_(DC)/2 186.Although illustrated as two steps 204 and 206, the steps of sampling andintegrating the filtered positive sense resistor voltage signal VRS_(P)_(—) lp 102 are continuous, with each new instantaneous voltage samplebeing used to update the integration, until the end of the one-halfperiod T_(DC)/2 186. Thus, for five hundred interrupts, the integrationstep is performed five hundred times.

An exponentially decaying transient waveform results upon initialapplication of either the positive injected DC voltage VDC_(P) 167portion or the negative injected DC voltage VDC_(N) 169 portion of thesquare wave. Further, as demonstrated above in Equation (4), the valueof the voltage across the sense resistor R_(S) 172 after application ofthe positive injected DC voltage VDC_(P) 167 is VRS_(PEAK)*e 1/τ, whereVRS_(PEAK) is the highest value of the exponentially decaying transientwaveform. For purposes of the insulation resistance R_(x) calculation,in order to effectively measure the final value of the positive senseresistor voltage VRS_(P) 165 a, it is necessary to wait until a value ofits exponentially decaying transient waveform has become negligible. Asquare wave switching frequency F_(DC) must therefore be selected toensure that the last voltage sample measured from the filtered positivesense resistor voltage signal VRS_(P) _(—) lp 102 (representative of thevoltage across the sense resistor R_(S) 172) at the end of thehalf-period is transient free.

To accomplish the last transient free voltage sample, the switchingfrequency F_(DC) of the square wave signal 164 is selected so that theone-half period T_(DC)/2186 is a multiple of the longest expected timeconstants. For example, if the one-half period T_(DC)/2 186 is selectedto be five times the time constant τ, a value of the exponentiallydecaying transient waveform decreases to a level within 1% of the steadystate or its final value at the end of expiration of the one-half periodT_(DC)/2186.

Integrating the positive sense resistor voltage VRS_(P) 165 a over theone-half period T_(DC)/2 186 yields:

$\begin{matrix}\begin{matrix}{{{integral}\lbrack {VRS}_{P} \rbrack} = {\int_{0}^{\frac{T_{DC}}{2}}{{VRS}_{PEAK}^{\frac{1}{\tau}}\ {t}}}} \\{= {{{- \tau}\; {VRS}_{PEAK}^{\frac{1}{\tau}}}|_{0}^{\frac{T_{DC}}{2}}}} \\{= {\tau \; {VRS}_{PEAK}}}\end{matrix} & (7)\end{matrix}$

Substituting the value of the pre-brush liftoff time constantτ_(FIRST)=(R+R_(S))*C_(FR) in the integral of the positive senseresistor voltage VRS_(P) 165 a yields a pre-brush liftoff integral:

integral[VRS _(P)]_(FIRST) =VRS _(PEAK)(R+R _(S))*C _(FR)  (8)

-   -   where VRS_(PEAK), R and R_(S) are constants having values fixed        by the circuit design. A pre-LPF proportionality constant        K_(C1), can be introduced in the Equation (6) such that the        integral of the positive sense resistor voltage VRS_(P) 165 a is        proportional to the capacitance value represented by the field        capacitor C_(FR):

integral[VRS _(P)]_(FIRST) =|integral[VRS _(N) ]|=K _(C1) C _(FR)  (9)

Equation (9) also illustrates that the absolute value of the integral ofthe negative sense resistor voltage VRS_(N) 165 b is equal to theintegral of the positive sense resistor voltage VRS_(P) 165 a.

As described in connection with Equation (6), the post-brush liftofftime constant τ_(SECOND) may be expressed as

$( {R + R_{S}} ){( \frac{C_{FR}*C_{RG}}{C_{FR} + C_{RG}} ).}$

Thus the integral of the positive sense resistor voltage VRS_(P) 165 aover the one-half period T_(DC)/2 during the brush liftoff condition maybe expressed as:

$\begin{matrix}\begin{matrix}{{{integral}\lbrack {VRS}_{P} \rbrack}_{SECOND} = | {{integral}\lbrack {VRS}_{N} \rbrack} |} \\{= {K_{C\; 1}( \frac{C_{FR}*C_{RG}}{C_{FR} + C_{RG}} )}}\end{matrix} & (10)\end{matrix}$

As described in connection with FIG. 7, the field ground module 100receives and processes the filtered positive sense resistor voltagesignal VRS_(P) _(—) lp 102 and the filtered negative sense resistorvoltage signal VRS_(N) _(—) lp 103 for purposes of providingfield-ground protection and for purposes of detecting a brush liftoff;it does not receive their corresponding unfiltered positive and negativesense resistor voltages VRS_(P) and VRS_(N). FIG. 9 is a functionalblock diagram 300 of a mathematical simulation that may be used toillustrate that inclusion of low-pass filter 171 in rotor assemblies150, 200 does not affect the proportionality between the integral ofeither the positive or negative sense resistor voltages 165 a, 165 b andthe capacitance between field winding 158 and electrical ground 154described in Equations (1)-(10).

Referring to FIG. 9, an exponentially decaying transient waveformgenerator 302 configured to generate the exponentially decayingtransient waveform such as exponentially decaying transient waveform 184and the exponentially decaying transient waveform 185 is provided. Afirst integration block 306 includes an input operatively coupled to anoutput generator 302 and is configured to perform an integration of thereceived exponentially decaying transient waveform. A low-pass 4^(th)order Butterworth filter 308 includes an input operatively coupled tothe output of generator 302 and is configured to receive theexponentially decaying transient waveform and to form a low-passfiltered waveform 312. Low-pass filter 308 may have a cut-off frequencyof 15.92 Hertz (Hz). A second integration block 310 includes an inputoperatively coupled to an output of filter 308 and is configured tointegrate the low-pass filtered waveform 312 to form an integratedfiltered transient waveform 311.

In operation, first integration is performed by the first integrationblock 306 by summing exponentially decaying transient waveform samplestaken at a rate of 1 kHz (one sample every millisecond). The firstintegration yields an integrated transient waveform 307. Theexponentially decaying transient waveform is also processed through thelow-pass filter 308 and then integrated via the second integration block310 to form the integrated filtered transient waveform 311. The resultsof the first and second integrations are listed in Table 1:

TABLE I Time- Capacity 1/Time- Integration I Integration II Constant (s)(microF) Constant (307) (311) 0.375 10 2.666666667 373.67 373.07 0.281257.5 3.555555556 281.52 281.02 0.1875 5 5.333333333 188 187.52 0.093752.5 10.66666667 94.25 93.77 0.0375 1 26.66666667 38 37.52 0.028125 0.7535.55555556 28.63 28.15 0.01875 0.5 53.33333333 19.25 18.77 0.0093750.25 106.6666667 9.88 9.4 0.00375 0.1 266.6666667 4.27 3.77 0.00281250.075 355.5555556 3.34 2.84 0.001875 0.05 533.3333333 2.42 1.9 0.00093750.025 1066.666667 1.52 0.963 0.000375 0.01 2666.666667 1.07 0.4

For further illustration, FIG. 10 is a graphical comparison of theintegrated transient waveform 307 and the integrated filtered transientwaveform 311. A plot of the integrated transient waveform 307 as afunction the field winding 158 to electrical ground 154 yields astraight line. Similarly, a plot of integrated filtered transientwaveform 311 as a function the field winding 158 to electrical ground154 yields a straight line. A comparison of the two plots indicates thatinclusion of the low-pass filter 171 in the synchronous generatorassemblies 150 and 200 does not affect the proportionality between theintegral of either the positive or negative sense resistor voltages 165a, 165 b and the capacitance between the field winding 158 andelectrical ground 154. It should be noted however that theproportionality between the integral of either the positive or negativesense resistor voltages 165 a, 165 b and the capacitance between thefield winding 158 and electrical ground 154 is slightly differentbetween the first integration and the second integration, as illustratedin FIG. 10.

Based on the above analysis and Equations (9) and (10), the integrals ofthe pre- and post-brush liftoff filtered positive sense resistor voltagesignal VRS_(P) _(—) lp 102 may be expressed as:

$\begin{matrix}\begin{matrix}{{{integral}\lbrack {{VRS}_{P}{\_ lp}} \rbrack}_{FIRST} = | {{integral}\lbrack {{VRS}_{N}{\_ lp}} \rbrack} |} \\{= {K_{C\; 2}C_{FR}}}\end{matrix} & (11) \\\begin{matrix}{{{integral}\lbrack {{VRS}_{P}{\_ lp}} \rbrack}_{SECOND} = | {{integral}\lbrack {{VRS}_{N}{\_ lp}} \rbrack} |} \\{= {K_{C\; 2}\frac{C_{FR}*C_{RG}}{C_{FR} + C_{RG}}}}\end{matrix} & (12)\end{matrix}$

Replacement of the pre-LPF proportionality constant K_(C1) with thepost-LPF proportionality constant K_(C2) confirms the small changebetween the constants of proportionality when the instantaneous voltageacross the sense resistor R_(S) 172 is measured at the output of thelow-pass filter rather than at the input. Referring again to FIG. 8,after integrating sample voltages of the filtered positive senseresistor voltage signal VRS_(P) _(—) lp 102 (step 206), microcontroller110 determines whether the end of the half-period T_(DC)/2 186 has beenreached (step 208). If the end of the half-period T_(DC)/2 186 has notbeen reached, the microcontroller awaits the next interrupt (step 210)and repeats steps 204, 206 and 208. If the end of the half-periodT_(DC)/2 186 has been reached, microcontroller 110 determines a value ofthe insulation resistor R_(x) 170 (step 211) and then determines whetherthe value of the insulation resistor R_(x) 170 indicates a loss of fieldwinding insulation (step 212) (see, Equation (1)).

As discussed in connection with FIG. 2, the insulation resistor R_(X)170 has a substantially infinite value when no loss of the field windinginsulation is indicated. If, however, resistor R_(X) 170 has a verysmall or zero value, loss of the field winding insulation is indicated.Referring again to FIG. 8, if the value of the insulation resistor R_(x)170 indicates a loss of field winding insulation (step 212), themicrocontroller 110 resets the integration to zero (step 220) and awaitsthe next interrupt (step 210). If the value of the insulation resistorR_(x) 170 indicates no loss of field winding insulation has occurred,the microcontroller 110 determines a capacitance between the fieldwinding 158 and the electrical ground 154, or a capacitance valuerepresented by the total capacitor C_(FG) 194.

Assuming that the pre-LPF and post-LPF proportionality constants K_(C1)and K_(C2) are determined experimentally, Equations (13) and (14)provide a basis for computing the capacitance between the field winding158 and the electrical ground 154 (i.e., a capacitance value representedby the total capacitor 194):

$\begin{matrix}{C_{FG} = {\frac{{integral}\lbrack {VRS}_{P} \rbrack}{K_{C\; 1}} = \frac{| {{integral}\{ {VRS}_{N} \}} |}{K_{C\; 1}}}} & (13)\end{matrix}$

or:

$\begin{matrix}{C_{FG} = {\frac{{integral}\lbrack {{VRS}_{P}{\_ lp}} \rbrack}{K_{C\; 2}} = \frac{| {{integral}\{ {{VRS}_{N}{\_ lp}} \}} |}{K_{C\; 2}}}} & (14)\end{matrix}$

Because the voltage samples used for the integration step 206 are basedon the filtered positive sense resistor voltage signal VRS_(P) _(—) lp102, the value of the total C_(FG) 194 is calculated using Equation (14)(step 214). When a brush liftoff situation occurs, the capacitancebetween the field winding 158 and the electrical ground 154 undergoes achange from a higher capacitance (i.e., the higher value of C_(FR) 174)to a much lower value (the lower value of C_(FR) 174 in series withC_(RG) 192). Referring again to FIG. 8, at step 214 after determiningthe capacitance value represented by capacitor C_(FG) 194, themicrocontroller 110 compares the value to a pre-selected thresholdsetting C_(SET). If the value is greater than the pre-selected thresholdsetting C_(SET), then no brush liftoff is declared (step 216) and theintegration is reset to zero (step 220). However, if the value is lessthan or equal to the pre-selected threshold value C_(SET), then brushliftoff is declared (step 218) and the integration is reset to zero(step 220). The microcontroller 100 may also cause an alarm indication.

Upon a determination of whether a brush liftoff has occurred during thehalf-period T_(DC)/2 186 in which the filtered positive sense resistorvoltage signal VRS_(P) _(—) lp 102 a was sampled and integrated, themicrocontroller 110 begins sampling and integrating the filterednegative sense resistor voltage signal VRS_(N) _(—) lp 102 b, and viceversa. In this way, the determination of whether a brush liftoff hasoccurred is performed twice for the time interval of one period T_(DC)185. It is contemplated however that the determination of whether abrush liftoff has occurred may also be performed more or less timesduring the time interval of one period T_(DC) 185, depending on the timeinterval selected for step 208.

The present method may be implemented as a computer process, a computingsystem or as an article of manufacture such as a computer programproduct or computer readable medium. The computer program product may bea computer storage media readable by a computer system and encoding acomputer program of instructions for executing a computer process. Thecomputer program product may also be a propagated signal on a carrierreadable by a computing system and encoding a computer program ofinstructions for executing a computer process.

In one embodiment, the logical operations of the present method areimplemented (1) as a sequence of computer implemented acts or programmodules running on a computing system and/or (2) as interconnectedmachine logic circuits or circuit modules within the computing system.The implementation is a matter of choice dependent on the performancerequirements of the computing system implementing the invention.Accordingly, the logical operations making up the embodiments of thepresent invention described herein are referred to variously asoperations, structural devices, acts or modules. It will be recognizedby persons skilled in the art that these operations, structural devices,acts and modules may be implemented in software, in firmware, in specialpurpose digital logic, and any combination thereof without deviatingfrom the spirit and scope of the present invention as recited within theclaims attached hereto.

While this invention has been described with reference to certainillustrative aspects, it will be understood that this description shallnot be construed in a limiting sense. Rather, various changes andmodifications can be made to the illustrative embodiments withoutdeparting from the true spirit, central characteristics and scope of theinvention, including those combinations of features that areindividually disclosed or claimed herein. Furthermore, it will beappreciated that any such changes and modifications will be recognizedby those skilled in the art as an equivalent to one or more elements ofthe following claims, and shall be covered by such claims to the fullestextent permitted by law.

1-29. (canceled)
 30. A method for detecting an open condition of agrounding path between a voltage source and electrical ground,comprising: applying a periodic oscillating voltage signal to a commonelectrical node between two terminals of the voltage source; calculatinga total capacitance between one of the voltage source and electricalground using the periodic oscillating voltage signal; and detecting theopen condition of the grounding path based on the total capacitance. 31.The method of claim 30, wherein the voltage source supplies voltage to afield winding.
 32. A system for detecting an open condition of agrounding path between a voltage source and electrical ground,comprising: a voltage source including two terminals; a signal generatorcoupled to a common electrical node between the two terminals,configured to apply a periodic oscillating voltage signal to the commonelectrical node; and a microcontroller programmed to calculate a totalcapacitance between the voltage source and electrical ground to detectthe open condition of the grounding path.
 33. The system of claim 32,wherein the voltage source supplies voltage to a field winding.
 34. Thesystem of claim 32, further comprising first and second buffer resistorscoupled at the common electrical node, the opposite sides of the firstand second resistors being coupled to respective terminals of thevoltage source.
 35. The system of claim 32, wherein the totalcapacitance equals an integrated value of a plurality of voltage samplesdivided by a proportionality constant, wherein the plurality of voltagesamples are derived from a filtered positive voltage signal during apositive one-half period of the periodic oscillating voltage signal anda filtered negative voltage signal during a negative one-half period ofthe periodic oscillating voltage signal.
 36. The system of claim 35,wherein the total capacitance C_(FG) equals:$C_{FG} = {\frac{{integral}\lbrack {{VRS}_{P}{\_ lp}} \rbrack}{K_{C\; 2}} = \frac{| {{integral}\lbrack {{VRS}_{N}{\_ lp}} \rbrack} |}{K_{C\; 2}}}$where VRS_(P) _(—) lp represents the filtered positive voltage signal,VRS_(N) _(—) lp represents the filtered negative voltage signal, andK_(C2) represents a proportionality constant.
 37. The system of claim36, wherein the proportionality constant is determined experimentally toenable the integrated value of the plurality of voltage samples to beproportional to the total capacitance.
 38. The system of claim 32,wherein the microcontroller is further programmed to: (a) cause aninterrupt at a predetermined time interval; (b) measure a value of afiltered positive voltage signal to form a voltage sample; (c) integratethe voltage sample over a positive one-half period of the periodicoscillating voltage signal to form a value of an integral of thefiltered positive voltage signal; (d) if an end of the positive one-halfperiod is reached, determine a value of an insulation resistance R_(X);(e) if the value of the insulation resistance R_(X) is infinite, dividethe value of the integral of the filtered positive voltage signal by aproportionality constant to calculate the total capacitance; and (f) ifthe total capacitance is less than a pre-selected capacitance setting,declare the open condition of the grounding path, and reset the value ofthe integral to zero.
 39. The system of claim 38, wherein themicrocontroller is further programmed to repeat steps (a)-(c) if the endof the negative one-half period is not reached.
 40. The system of claim38, wherein the microcontroller is further programmed to reset the valueof the integral to zero if the value of the insulation resistance is notinfinite.
 41. The system of claim 38, wherein the microcontroller isfurther programmed to: not declare the open condition of the groundingpath if the total capacitance is not less than the pre-selectedcapacitance setting; and reset the value of the integral to zero. 42.The system of claim 32, wherein the periodic oscillating voltage signalcomprises a square wave voltage signal.
 43. The method of claim 30,further comprising: comparing the total capacitance to a pre-selectedcapacitance setting if, at the end of a one-half period of the periodicoscillating voltage signal, a resistance value between the voltagesource and electrical ground is substantially infinite; declaring theopen condition of the grounding path if the total capacitance is lessthan the pre-selected capacitance setting; and not declaring the opencondition of the grounding path if the total capacitance is greater thanthe pre-selected capacitance setting.
 44. The method of claim 43,further comprising: during the one-half period, deriving a plurality ofvoltage samples from one of a positive voltage and a negative voltagegenerated across a sense resistor, the sense resistor operativelycoupling a generator of the periodic oscillating voltage signal toelectrical ground; integrating a value of the plurality of voltagesamples to form an integrated value; and dividing the integrated valueby a proportionality constant to calculate the total capacitance. 45.The method of claim 44, wherein the plurality of voltage samples aremeasured from a filtered negative sense resistor voltage signal during anegative one-half period of the periodic oscillating voltage signal, thefiltered negative sense resistor voltage signal resulting from filteringthe negative voltage generated across the sense resistor.
 46. The methodof claim 44, wherein the plurality of voltage samples are measured froma filtered positive sense resistor voltage signal during a positiveone-half period of the periodic oscillating voltage signal, the filteredpositive sense resistor voltage signal resulting from filtering thepositive voltage generated across the sense resistor.
 47. The method ofclaim 30, wherein the total capacitance C_(FG) equals:$C_{FG} = {\frac{{integral}\lbrack {{VRS}_{P}{\_ lp}} \rbrack}{K_{C\; 2}} = \frac{| {{integral}\lbrack {{VRS}_{N}{\_ lp}} \rbrack} |}{K_{C\; 2}}}$where VRS_(P) _(—) lp represents a filtered positive sense resistorvoltage signal derived from a positive voltage generated across a senseresistor operatively coupling a generator of the periodic oscillatingvoltage signal to electrical ground, VRS_(N) _(—) lp represents afiltered negative sense resistor voltage signal derived from a negativevoltage generated across the sense resistor, and K_(C2) represents aproportionality constant.
 48. The method of claim 47, further comprisingexperimentally determining the proportionality constant.
 49. The methodof claim 30, wherein the periodic oscillating voltage signal comprises asquare wave voltage signal.